Uniform ergodic theorems on aperiodic linearly repetitive tilings and applications

被引：5
作者：
Besbes, Adnene [1 ]
机构：
[1] Univ Paris Diderot, F-75013 Paris, France
来源：
REVIEWS IN MATHEMATICAL PHYSICS | 2008年 / 20卷 / 05期
关键词：
tiling; ergodic; linear repetitivity;
D O I：
10.1142/S0129055X0800333X
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The paper is concerned with aperiodic linearly repetitive tilings. For such tilings, we establish a weak form of self-similarity that allows us to prove general (sub) additive ergodic theorems. Finally, we provide applications to the study of lattice gas models.
引用
收藏
页码：597 / 623
页数：27
相关论文
共 21 条
[1]  
BAAKE M, 2000, CRM MONOGRAPH SERIES, V13, P371
[2]   Linear repetitivity, I. Uniform subadditive ergodic theorems and applications [J].
Damanik, D ;
Lenz, D .
DISCRETE & COMPUTATIONAL GEOMETRY, 2001, 26 (03) :411-428
[3]   Linearly recurrent subshifts have a finite number of non-periodic subshift factors [J].
Durand, F .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2000, 20 :1061-1078
[4]   Linearly recurrent subshifts have a finite number of non-periodic factors (vol 20, pg 1061, 2000) [J].
Durand, F .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2003, 23 :663-669
[5]  
Geerse C. P. M., 1991, Reviews in Mathematical Physics, V3, P163, DOI 10.1142/S0129055X91000072
[6]  
Georgii H.-O., 1988, Gibbs Measures and Phase Transitions
[7]   SOME REMARKS ON DISCRETE APERIODIC SCHRODINGER-OPERATORS [J].
HOF, A .
JOURNAL OF STATISTICAL PHYSICS, 1993, 72 (5-6) :1353-1374
[8]  
ISRAEL RB, 1979, CONVEXITY THEORY LAT
[9]  
Janot C., 1997, Quasicrystals: a primer
[10]   Repetitive Delone sets and quasicrystals [J].
Lagarias, JC ;
Pleasants, PAB .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2003, 23 :831-867
123